Calculus of Variations and Geometric Measure Theory

N. Ansini - A. Braides

Asymptotic analysis of periodically-perforated nonlinear media

created on 09 Mar 2001
modified by ansini on 05 Dec 2005


Published Paper

Inserted: 9 mar 2001
Last Updated: 5 dec 2005

Journal: J. Math. Pures Appl.
Volume: 81
Pages: 439-451
Year: 2002


We propose a direct approach to the study of the asymptotic behaviour of Dirichlet problems in perforated domains giving rise to extra terms. As an application, we give a proof of the non-linear vector-valued variational version of the Cioranescu Murat result. Our method is based on a lemma which allows to modify sequences of functions in the vicinity of the perforation, in the spirit of a method proposed by De Giorgi to match boundary conditions. We describe the extra term by a capacitary formula involving a quasiconvexification process. Non-existence and non-positive homogeneity phenomena are discussed.

Keywords: Gamma-limits, perforated domains, nonlinear capacity, Relaxed Dirichlet Problems